Tracing the redshift evolution of Hubble parameter with gravitational-wave standard sirens

Proposed space-based gravitational-wave detectors such as BBO and DECIGO can detect similar to 10(6) neutron star (NS) binaries and determine the luminosity distance to the binaries with high precision. Combining the luminosity distance and electromagnetically derived redshift, one would be able to probe cosmological expansion out to high redshift. In this paper, we show that the Hubble parameter as a function of redshift can be directly measured with monopole and dipole components of the luminosity distance on the sky. As a result, the measurement accuracies of the Hubble parameter in each redshift bin up to z = 1 are 3-14%, 1.5-8%, and 0.8-4% for the observation time 1 yr, 3 yr, and 10 yr, respectively.